How do you remove discontinuity of #f(x) = (x^4 - 1)/(x-1)#?

Answer 1
You can write your numerator as #(x^2-1)(x^2+1)# where #(x^2-1)=(x-1)(x+1)# giving: #f(x)=((x-1)(x+1)(x^2+1))/(x-1)=(x+1)(x^2+1)#
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Answer 2

To remove the discontinuity of the function f(x) = (x^4 - 1)/(x-1), we can use algebraic manipulation. The function has a discontinuity at x = 1 because the denominator becomes zero at that point. To remove this discontinuity, we can factorize the numerator as a difference of squares: x^4 - 1 = (x^2 + 1)(x^2 - 1). Then, we can simplify the function as f(x) = (x^2 + 1)(x^2 - 1)/(x-1). Now, we can cancel out the common factor of (x-1) in the numerator and denominator, resulting in f(x) = (x^2 + 1)(x + 1). This new function, f(x) = (x^2 + 1)(x + 1), does not have a discontinuity at x = 1.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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